Activity 30

MATH 216: Statistical Thinking

Comprehensive Statistical Test Selection Framework

Time Allocation: 15 minutes total (5 min reading, 10 min individual work)

Part 1: Conceptual Understanding (3 minutes)

Instructions: Answer the following questions based on the lecture content:

  1. What are the key decision factors for selecting between parametric and nonparametric statistical tests, and how do these factors influence test choice?
  1. Explain the decision framework for choosing between one-sample tests (z-test, t-test, sign test, Wilcoxon signed-rank) based on data characteristics and research design.
  1. How does the choice between independent samples t-test (pooled vs Welch’s) and Mann-Whitney U test depend on data distribution and variance characteristics?

Part 2: Real Data Analysis with R Output (4 minutes)

Analyze real datasets and interpret R test output for different scenarios:

Scenario 1: Exercise Program Effectiveness

A fitness center tests if their new exercise program reduces resting heart rate. They measure heart rates (bpm) for 15 participants before and after the program:

Before: 72 75 80 68 82 74 78 71 76 79 73 77 70 81 69 
After: 68 72 76 65 78 70 75 68 73 76 70 74 67 77 66

R paired t-test output:

Paired t-test

data:  before and after
t = 8.94, df = 14, p-value = 2.45e-07
alternative hypothesis: true mean difference is less than 0
95 percent confidence interval:
 -Inf -3.28
sample estimates:
mean difference
         -3.73
  • What test was used and why was it appropriate?
  • State the statistical decision at α = 0.05
  • Interpret the practical significance

Scenario 2: Online vs Traditional Classroom Performance

A university compares exam scores between online and traditional classroom formats:

Online (n=14): 78 82 83 87 75 43 78 42 94 47 98 90 97 81 
Traditional (n=12): 83 82 92 100 74 90 44 84 77 89 70 34

R Mann-Whitney test output:

Wilcoxon rank sum test with continuity correction

data:  online_scores and traditional_scores
W = 78, p-value = 0.847
alternative hypothesis: true location shift is not equal to 0
  • Why was Mann-Whitney test chosen instead of a t-test?
  • What is the statistical conclusion?
  • What does this mean for educational policy?

Scenario 3: Manufacturing Process Comparison

A factory compares production efficiency between two assembly lines:

Line A (n=10): mean = 45.9 sd = 2.9 
Line B (n=10): mean = 43 sd = 3.3

R Welch’s t-test output:

Welch Two Sample t-test

data:  line_a and line_b
t = 2.15, df = 17.8, p-value = 0.045
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
 0.08 3.92
sample estimates:
mean of x mean of y
     45.9      43.0
  • Why was Welch’s test used instead of pooled t-test?
  • What is the statistical decision?
  • Interpret the confidence interval

Part 3: Decision Making and Interpretation (3 minutes)

Evaluate test selection decisions and interpret consequences:

  1. For the exercise program scenario, what would be the consequences of using an independent samples t-test instead of the paired t-test?
  1. For the classroom comparison scenario, what additional information would help you decide between Mann-Whitney and Welch’s t-test?
  1. For the manufacturing scenario, what practical recommendations would you make based on the statistical results?